Detection of Electron Paramagnetic Resonance Spectra of Optically Induced Carriers with the Properties of the Effective Mass in the WS₂ Transition Metal Dichalcogenide

The spin properties of transition metal dichalcogenides are of interest for applications in spintronics. Anisotropic electron paramagnetic resonance spectra in a WS₂ single crystal under optical excitation have been detected. These spectra assumingly belong to localized carriers near the valence band and reflect features of the 5d shell of the crystal. It has been shown that the g-factor for the magnetic field perpendicular to the c‑axis of the crystal (in-plane magnetic field) is larger than that for the magnetic field parallel to the c‑axis (perpendicular to the layer plane), which can provide information on the type of the 5d function. The discussed center is most likely described by the $5d({{z}^{2}} - {{r}^{2}})$ wavefunction, which can be associated with the valence band of the crystal.

Two-dimensional materials have a number of unique properties making them attractive for the application in numerous microelectronic devices. Interest in two-dimensional materials was initiated by active studies of two-dimensional graphene [1]. Since graphene does not have a band gap, its application in electronics and optics is limited. Semiconducting compounds of W and Мо with S and Se, so-called transition metal dichalcogenides, e.g., MoS₂ and WS₂, are currently considered as very promising highly efficient functional nanomaterials because of their specific two-dimensional layered structure. Two-dimensional materials have a layered crystal structure with tight bonds in the plane where layers are coupled with each other by weak van der Waals forces [2–6]. These materials are promising candidates for opto- and nanoelectronics because of a nonzero band gap, photosensitivity, and extraordinary electronic and optical properties.

The strong spin–orbit coupling caused by d electrons involved in the formation of chemical bonds leads to the spin splitting of bands and makes transition metal dichalcogenides promising for applications in spintronics [7]. Coupled spin and valley degrees of freedom in transition metal dichalcogenides are considered as an attractive platform for information processing [8].

A series of nominally pure bulk WS₂ crystals with a thickness about hundreds of microns were grown by chemical vapor deposition. Samples with average sizes of about 2 × 2 × 0.1 mm were chosen for the study; the sizes and thicknesses of samples were varied in different experiments. To measure Raman scattering and photoluminescence (PL), we used a confocal microscope (NT-MDT SI) equipped with a spectrometer (SOL Instruments) and a CCD matrix (Andor) with the spectral range of 200–1100 nm and a resolution of 0.7 cm^–1 for Raman scattering and of 0.7 nm for PL. A ×100 microscope objective with a numerical aperture of NA = 0.7 and a 1-mm pinhole was used to collect a signal from a volume of about 5 μm³. Optical excitation at a power of about 1 mW for the detection of Raman and PL spectra was carried out by a semiconductor laser with a wavelength of $\lambda = 532{\kern 1pt}$ nm (the setup is described in [9]). Electron paramagnetic resonance (EPR) studies were performed on the unique line of high-frequency EPR/ODMR spectrometers (94 and 130 GHz), which were developed at the Ioffe Institute together with the DOC firm (the setup is described in [10, 11]). We used a magneto-optical system with a closed-cycle cryostat, which allowed the variation of the magnetic field from –7 to +7 T with a smooth passage through zero; the temperature range was 1.5–300 K.

The sketch of the crystal structure of the bulk 2-H‑WS₂ material is shown in Fig. 1a, where the main distances between atoms and an interlayer distance of 0.618 nm are indicated and photographs of two samples from the studied series are presented. Raman scattering and PL are efficient noninvasive tools to study semiconductor transition metal dichalcogenides. Figure 1b shows the experimental Raman spectrum detected from the studied bulk WS₂ crystal at room temperature in comparison with Raman spectra in WS₂ materials from [12]. It is seen that our Raman spectra and data from [12] indicate a fairly high quality of the material under study. This quality is also confirmed by PL studies of the bulk WS₂ crystal using confocal optics. The PL spectrum detected from the studied bulk WS₂ crystal excited by the 532-nm laser at room temperature is presented in Fig. 1c. The lower part of Fig. 1c shows typical PL spectra in bulk and monolayer WS₂ materials taken from [13], which indicate the presence of the main PL lines of this material in our spectra. Fragments of the upper part of the valence band (VB) and the lower part of the conduction band (CB) for the (red solid lines) bulk and (blue dashed lines) monolayer WS₂ materials are schematically shown in the right part of Fig. 1c, where arrows indicate the indirect and direct transitions for the bulk and monolayer materials, respectively.

Fig. 1.

(Color online) (а) Sketch of the crystal structure of the bulk 2H-WS₂ material; the inset shows photographs of two samples from the studied series. (b) Experimental Raman spectrum detected from the studied bulk WS₂ crystal at room temperature and data on Raman spectra in WS₂ taken from [12]. (c) Photoluminescence spectrum detected from the bulk WS₂ crystal excited by 532-nm laser radiation at room temperature; the bottom part presents data on typical photoluminescence spectra in bulk and monolayer WS₂ materials taken from [13]; the right part schematically shows fragments of the top of the valence band and the bottom of the conduction band for the (red solid lines) bulk and (blue dashed lines) monolayer materials.

Monolayer transition metal dichalcogenides samples were also studied on our confocal microscope for the calibration of the PL intensity. With the unification of the experimental parameters (laser power, diameter of the pinhole of the confocal system, and signal acquisition time), it was shown that the PL intensity in the bulk material is about four or five orders of magnitude lower than that in the monolayer material. This relation is a natural consequence of the band structure of the bulk and monolayer WS₂ materials (see Fig. 1с).

Figure 2a presents the angular dependence of EPR spectra, which consist of three optically induced lines with different intensities (photo-EPR), at a frequency of 94 GHz and a temperature of 5 K. In this magnetic field region, EPR signals were not observed in the absence of irradiation.

Fig. 2.

(Color online) (a) Angular dependence of EPR spectra consisting of three lines with different intensities induced by optical radiation (photo-EPR) at a frequency of 94 GHz and a temperature of 5 K. The right axis represents the angle between the direction of the magnetic field and the c-axis of symmetry, which is perpendicular to the plane of the crystal. The inset shows the angular dependence of the photo-EPR spectrum at a frequency of 130 GHz and a temperature of 5 K. (b) Time dependence of the measured EPR signal intensity after the end of laser irradiation; the observed decrease is due to the recombination of light-induced electron–hole pairs. The red dashed line corresponds to the empirical Becquerel equation. (с) Temperature dependence of the photo-EPR signal intensity under continuous laser irradiation. The red dashed line is a simulated curve close to a hyperbolic curve corresponding to the Curie law.

Electron paramagnetic resonance spectra are described by the following spin Hamiltonian representing the electron Zeeman interaction for an axially symmetric paramagnetic center in the magnetic field [14]:

$$\hat {H} = {{\mu }_{{\text{B}}}}\mathbf{B} \cdot \mathbf{g} \cdot \hat {\mathbf{S}} = {{\mu }_{{\text{B}}}}[{{g}_{\parallel }}{{B}_{z}}{{\hat {S}}_{z}} + {{g}_{ \bot }}({{B}_{x}}{{\hat {S}}_{x}} + {{B}_{y}}{{\hat {S}}_{y}})].$$

(1)

Here, μ_B is the Bohr magneton, $\hat {\mathbf{S}}$ is the S = 1/2 spin operator of the electron, and ${{g}_{\parallel }}$ and ${{g}_{ \bot }}$ are the components of the anisotropic electron g-factor.

The dotted lines in Fig. 2a are the dependences calculated by the formula ${{g}^{2}} = g_{\parallel }^{2}{{\cos }^{2}}\theta + g_{ \bot }^{2}{{\sin }^{2}}\theta$, where $\theta$ is the angle between the direction of the magnetic field and the c-axis of symmetry, which is perpendicular to the crystal layer. For the magnetic field perpendicular to the c axis (θ = 90°, $B \bot c$), the g-factors for all three lines are the same ${{g}_{ \bot }} = 2.698$ within the experimental accuracy. The intensity of the EPR lines decreases with the deviation of θ from 90°, and lines almost disappear at θ < 50°. For this reason, the g-factors g_|| for θ = 0° were calculated by the above formula: g_||1 = 2.181 and g_||2 = 2.124 for the more and less intense lines, respectively. Similar angular dependences of three EPR signals were observed at the rotation of the crystal in the plane perpendicular to the c axis, which indicates the absence of a lower symmetry of the paramagnetic center. Several reasons are possible for the splitting of EPR lines. The simplest reason is a certain imperfection of the crystal, which results in an insignificant separation of the material (less than 1°). The presence of several polytypes of the material is also not excluded because it is known that three structural WS₂ phases including the 2H, 3R, and 1T polytypes can be implemented, depending on the arrangement of layers [15]. We also recorded the angular dependences of photo-EPR signals at a frequency of 130 GHz and obtained similar parameters of EPR spectra; i.e., the spin Hamiltonian (1) with the spin S = 1/2 describes the experimental data at both frequencies. The inset of Fig. 2a shows the fragment of the angular dependence of the photo-EPR spectrum at a frequency of 130 GHz and a temperature of 5 K. The spectra were detected under the same conditions with the simple replacement of the microwave unit. The ratio of the magnetic fields, e.g., for EPR signals for the perpendicular orientation of magnetic fields of 3.44 and 2.49 T at frequencies of 130 and 94 GHz, respectively, is 1.38, which corresponds to the ratio of frequencies, thus excluding the presence of possible additional interactions affecting the Zeeman splitting of levels.

Figure 2b presents the time dependence of the measured EPR signal intensity after the end of laser irradiation; the observed decrease is due to the recombination of light-induced electron–hole pairs. The red dashed line corresponds to the empirical Becquerel formula $I = a{{t}^{b}}$. The coefficient b in this formula calculated for the hyperbolic segment of the curve is ‒0.4. The Becquerel formula describes recombination luminescence, and the decrease in the intensity in the general case corresponds to the second-order kinetics. We used this equation to describe the recombination of long-lived paramagnetic centers, which were formed under laser irradiation and were detected by the EPR signal. A fractional order obtained in experiments can be due both to features of the diffusion of photoexcited centers and to the presence of several centers or several recombination channels.

Figure 2c shows the temperature dependence of the photo-EPR signal intensity under continuous laser irradiation. The red dashed line is a simulated curve close to a hyperbolic curve corresponding to the Curie law $I \propto {{T}^{{ - 1}}}$. The anisotropy of the g-factor is directly related to the spin–orbit coupling, which is giant in a heavy element such as tungsten W. It is noteworthy that EPR studies are primarily carried out for transition elements [16]; for this reason, studies of crystals whose band structure is formed by transition elements and which are not magnetic materials (i.e., their electron shells are completely filled) are of particular interest. The interband optical excitation leads to the formation of electron–hole pairs, which are paramagnetic.

In the presence of the axial symmetry, the following formula can be used for the g-factor depending on the angle between the magnetic field direction and the axis of the paramagnetic center if the lower energy state is an orbital singlet and, as a result, the orbital angular momentum is frozen in the ground state [14, 16]:

$${{g}_{{zz}}} = {{g}_{s}} + 2\lambda {{\Lambda }_{{zz}}} = {{g}_{s}} - 2\lambda \sum\limits_n '\frac{{\langle 0{\text{|}}{{{\hat {L}}}_{x}}{\text{|}}n\rangle \langle n{\text{|}}{{{\hat {L}}}_{z}}{\text{|}}0\rangle }}{{E_{n}^{{(0)}} - E_{0}^{{(0)}}}} = {{g}_{s}},$$

$${{g}_{{xx}}} = {{g}_{s}} + 2\lambda {{\Lambda }_{{xx}}}$$

$$ = {{g}_{s}} - 2\lambda \sum\limits_n '\frac{{\langle 0{\text{|}}{{{\hat {L}}}_{x}}{\text{|}}n\rangle \langle n{\text{|}}{{{\hat {L}}}_{x}}{\text{|}}0\rangle }}{{E_{n}^{{(0)}} - E_{0}^{{(0)}}}} = {{g}_{s}} - \frac{{2\lambda }}{\delta },$$

$${{\Lambda }_{{ij}}} = - \sum\limits_n '\frac{{\langle 0{\text{|}}{{{\hat {L}}}_{i}}{\text{|}}n\rangle \langle n{\text{|}}{{{\hat {L}}}_{j}}{\text{|}}0\rangle }}{{E_{n}^{{(0)}} - E_{0}^{{(0)}}}}.$$

(2)

Here, ${{g}_{s}} = 2.0023$, λ is the spin–orbit coupling constant, and $\delta$ is the average splitting between the ground and excited energy levels $[E_{n}^{{(0)}}]$ in the crystal field. This result was obtained by representing the orbital angular momentum operator L in the form of the raising and lowering operators for particular d wavefunctions of this problem. The qualitative analysis of Eq. (2) shows that the g-factor is anisotropic and has different components for the magnetic field parallel and perpendicular to the axis of symmetry, which depend on the contribution from the orbital angular momentum for the excited state:

$${{g}_{\parallel }} = {{g}_{s}};\quad {{g}_{ \bot }} = {{g}_{s}} - 2\lambda {\text{/}}\delta .$$

The spin–orbit coupling constant for free ions with d electrons is $\lambda > 0$ and $\lambda < 0$ if the d shell is less and more than half-filled, respectively. The relation between ${{g}_{ \bot }}$ and ${{g}_{\parallel }}$ depends on the magnitude and sign of the spin–orbit coupling constant in the WS₂ crystal, which differ from the respective parameters for the free ion. In our experiments, ${{g}_{ \bot }} > {{g}_{\parallel }}$, which can be analyzed theoretically by considering the properties of a localized hole near the top of the valence band.

Figure 3 presents schematically the energy diagram for the bulk 2H-WS₂ crystal. The process of photoabsorption for the generation of photoelectrons in the conduction band and photoholes in the valence band of 2H-WS₂ is illustrated. Two arrows on 5d orbitals in the valence band represent the initial 5d electrons on the W atom. The scheme in Fig. 3 is a conditional modification of the scheme presented for 2H-MoS₂ in [17]. The right part of Fig. 3 demonstrates the transition of one electron to the conduction band and the corresponding EPR signal from the hole remaining in the valence band. Further, after the end of laser irradiation, the recombination of the electron–hole pair occurs in several minutes, and the EPR signal disappears. The EPR signal from the center in the conduction band was not yet detected probably because of the strong delocalization of the electron in the conduction band.

Fig. 3.

(Color online) Conditional energy diagram for the bulk 2H-WS₂ crystal. The process of photoabsorption for the generation of photoelectrons in the conduction band (CB) and photoholes in the valence band (VB) of 2H-WS₂ is illustrated. Arrows on 5d orbitals represent the two initial 5d electrons on the W atom. The right part demonstrates the transition of one electron to the conduction band and the corresponding EPR signal from the hole remaining in the valence band. Further, after the end of laser irradiation, the recombination of the electron–hole pair occurs in several minutes, and the EPR signal disappears.

As shown in Fig. 3, 2H-WS₂ has D_3h symmetry, and its crystal field splits five W 5d orbitals into three groups: the $5d({{z}^{2}} - {{r}^{2}})$ orbital, which is the most stable, followed by two degenerate $5d(xz)$ and $5d(yz)$ orbitals and two degenerate $5d({{x}^{2}} - {{y}^{2}})$ and $5d(xy)$ orbitals (by analogy with the scheme presented for MoS₂ in [17]. The W ion has a degree of oxidation of +4 and has two 5d electrons both in the lowest $5d({{z}^{2}} - {{r}^{2}})$ orbital, whereas higher 5d orbitals are empty. Because of the complete filling of the $5d({{z}^{2}} - {{r}^{2}})$ orbital, which corresponds to the valence band in its band structure, 2H-WS₂ is a semiconductor material.

The density functional theory calculations in [18] show that the valence band at the Γ point of WS₂ or-iginates primarily from W $5d({{z}^{2}} - {{r}^{2}})$ orbitals and S $3p(z)$ orbitals. As the thickness of transition metal dichalcogenides increases from the monolayer to the bulk material, the interaction between packed WS₂ layers first results in the appearance of a sequence of subbands near the top of the valence band. Finally, these subbands in the bulk material are joined in a bulk band (see Fig. 3). Since the top of the valence band is located at the point $\Gamma$ in the bulk material, the distance and effective hole mass of this sequence bands are important for the determination of the general electronic properties of the layered WS₂ material.

A giant spin–orbit splitting in the upper part of the valence band is one of the most important properties of WS₂ for spintronic applications. The spin–orbit splitting increases with the atomic number Z of the transition metal because the top of the valence band originates predominantly from the d shell of the transition metal. This splitting also insignificantly depends on the thickness of the material and varies in the range of 425–577 meV [18]. The experimentally determined spin–orbit splitting is ~450 meV for the bulk WS₂ (0001) crystal and is ~200 and 500 meV for MoS₂ and WSe₂, respectively; i.e., it is seen that the transition metal makes the main contribution to the spin–orbit splitting [18]. The spin–orbit splitting of levels in the conduction band is more than an order of magnitude smaller than the splitting in the valence band. This relation also supports our attribution of the observed photo-EPR spectra to hole centers near the top of the valence band. The conventional EPR technique cannot be used to study WS₂ monolayers because of its rather low sensitivity, but the presence of strong PL in these structures allows us to expect that optically detected magnetic resonance (ODMR) of carriers and excitons can be observed in WS₂ monolayers owing to the giant spin–orbit coupling for W 5d electrons.

To summarize, we have detected anisotropic EPR spectra in the WS₂ single crystal under optical excitation. These spectra have been attributed to localized carriers near the valence band and reflect features of the 5d shell of the crystal. It has been shown that the g‑factor for the magnetic field perpendicular to the axis of symmetry of the crystal (in-plane magnetic field) is larger than that for the magnetic field parallel to the axis of symmetry (perpendicular to the layer plane), which can provide information on the type of the 5d function near the top of the valence band. The discussed center is most likely described by the $5d({{z}^{2}} - {{r}^{2}})$ wavefunction, which can be associated with the valence band of the crystal. After the end of irradiation, a comparatively slow recombination of electron–hole pairs occurs and the EPR spectrum disappears in several minutes at a temperature of about 5 K.